In the Idea of Limits video, we introduce the idea of limits and discuss how it underpins all of the major concepts in calculus. In the Limit Laws video, we introduce the limit laws and discuss how to ...

In this page, we introduce a differential based method for vector and matrix derivatives (matrix calculus), which only needs a few simple rules to derive most matrix derivatives. This method is useful ...

This repository contains tutorial handouts and supporting materials (LaTeX source files and figures) for HKUST MATH1014 (Calculus II), 2026 Spring. Note: MATH1014 has multiple tutorial sessions and ...

Faltings’ Theorem ️ It explains why certain algebraic equations have only a limited number of solutions, even though numbers themselves go on forever. Imagine a curve drawn by a polynomial ...

Prerequisites: Credit for MATH 2312 with a grade of C- or higher, or a satisfactory score on a placement examination. Course Description: Calculus of single variable functions, limits, continuity, ...

In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

Limit and Continuity: These ideas gained clarity and rigor in the 17th century with the independent development of calculus by Isaac Newton and Gottfried Wilhelm Leibniz. Later, Augustin-Louis Cauchy ...